1. 1.2 Units of Length, Mass, and Time
Chapter 1
1.2 Units of Length, Mass, and Time

2. 1.2 Units of Length, Mass, and Time
Length, Mass, and Time are the fundamental quantities used to describe the Physical World.
All other quantities such as Force, Energy, Power, and, velocity are derived from these 3 base units.

3. 1.2 Units of Length
Early units of distance were often associated with the human body.
An Egyptian cubit was the distance from the elbow to the tip of the middle finger.
The foot was defined as the length of the royal foot of King Louis XIV of France.
The precise origin of the Yard is not definitely known. Some claim that the measure was invented by Henry I of England as being the distance between the tip of his nose and the end of his thumb.

4. 1.2 Units of Length
The question of measurement reform was placed in the hands of the Academy of Sciences who appointed a commission chaired by Jean-Charles de Borda.
This commission decided that the new measure should be equal to one ten-millionth of the distance from the North Pole to the Equator (the quadrant of the Earth's circumference), measured along the meridian passing through Paris.

5. 1.2 Units of Length The S.I. unit of length is the Meter.
[1]
The S.I. unit of length is the Meter.
1⁄10,000,000 part of the quarter of a meridian, measurement (North Pole to Equator) (1793)
Platinum-iridium bar at melting point of ice, atmospheric pressure, supported by two rollers (1927)
1,650, wavelengths of light from a specified transition in krypton-86 (1960)
Length of the path travelled by light in a vacuum in 1⁄299,792,458 of a second (1983)

6. Table 1-1 Typical Distances
Distance from the Earth to the nearest large galaxy (the Andromeda Galaxy, M31)
2 x 1022 m
Diameter of our galaxy (the Milky Way)
8 x 1020 m
Distance from the Earth to the nearest star (other than the Sun)
4 x 1016 m
One light year
9.46 x 1015 m
Average radius of Pluto’s orbit
6 x 1012 m
Distance from Earth to the Sun
1.5 x 1011 m
Radius of Earth
6.37 x 106 m
Length of football field
102 m
Height of a person
2 m
Diameter of a CD
0.12 m
Diameter of the aorta
0.018 m
Diameter of the period in a sentence
5 x 10–4 m
Diameter of a red blood cell
8 x 10–6 m
Diameter of the hydrogen atom
10–10 m
Diameter of a proton
2 x 10–15 m

7. 1.2 Units of Mass The S.I. unit of Mass is a kilogram.
The gram was originally defined in 1795 as the mass of one cubic centimeter of water at 4 °C, making the kilogram equal to the mass of one liter of water.
The kilogram is currently defined as the mass of a particular platinum-iridium alloy cylinder at eh International Bureau of Weights and Standards in Sevres, France.

8. 1.2 Units of Mass
The kilogram is the only SI base unit with an SI prefix ("kilo", symbol "k") as part of its name.
It is also the only SI unit that is still directly defined by an artifact rather than a fundamental physical property that can be reproduced in different laboratories.

9. Table 1-2 Typical Masses
Galaxy (Milky Way)
4 x 1041 kg
Sun
2 x 1030 kg
Earth
5.97 x 1024 kg
Space Shuttle
2 x 106 kg
Elephant
5400 kg
Automobile
1200 kg
Human
70 kg
Baseball
0.15 kg
Honeybee
1.5 x 10–4 kg
Red blood cell
10–13 kg
Bacterium
10–15 kg
Hydrogen atom
1.67 x 10–27 kg
Electron
9.11 x 10–31 kg

10. 1.2 Units of Time The S.I. unit of time is the Second.
The Egyptians subdivided daytime and nighttime into twelve hours each since at least 2000 BC, hence the seasonal variation of their hours.
The Hellenistic astronomers Hipparchus (c. 150 BC) and Ptolemy (c. AD 150) subdivided the day sexadesimally and also used a mean hour (1⁄24 day), simple fractions of an hour (1⁄4, 2⁄3, etc.) and time-degrees (1⁄360 day or four modern minutes), but not modern minutes or seconds.

11. 1.2 Time
The earliest clocks to display seconds appeared during the last half of the 16th century.
In 1581, Tycho Brahe redesigned clocks that displayed minutes at his observatory so they also displayed seconds. However, they were not yet accurate enough for seconds. In 1587, Tycho complained that his four clocks disagreed by plus or minus four seconds.

12. 1.2 Time
The second first became accurately measurable with the development of pendulum clocks keeping mean time (as opposed to the apparent time displayed by sundials).
In 1956, the second was redefined in terms of a year: the fraction 1/31,556, of the tropical year for 1900 January 0 at 12 hours ephemeris time.

13. 1.2 Time
In 1960 the second was defined as the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom.
This is the modern definition and the basis for atomic clocks.

14. Table 1-3 Typical Times
Age of the universe
5 x 1017 s
Age of the Earth
1.3 x 1017 s
Existence of human species
6 x 1013 s
Human lifetime
2 x 109 s
One year
3 x 107 s
One day
8.6 x 104 s
Time between heartbeats
0.8 s
Human reaction time
0.1 s
One cycle of a high-pitched sound wave
5 x 10–5 s
One cycle of an AM radio wave
10–6 s
One cycle of a visible light wave
2 x 10–15 s

15. Table 1-4 Common Prefixes
Power
Prefix
Abbreviation
1015
peta P
1012
tera T
109
giga G
106
mega M
103
kilo k
102
hecto h
101
deka da
10–1
deci d
10–2
centi c
10–3
milli m
10–6
micro
10–9
nano n
10–12
pico p
10–15
femto f